The perimeters of two similar ΔABC and ΔPQR are 48.4 cm and 12.1 cm, respectively. What is the ratio of the areas of ΔABC and ΔPQR ?

16 : 1

Formula Used

\(\frac{Area\; of\; ΔABC}{Area\; of\; ΔPQR}\) = (\(\frac{Perimeter\; of\; ΔABC}{Perimeter\; of\; ΔPQR}\))²

Calculations

\(\frac{Area\; of\; ΔABC}{Area\; of\; ΔPQR}\) = (\(\frac{48.4}{12.1}\))²

\(\frac{Area\; of\; ΔABC}{Area\; of\; ΔPQR}\) = (\(\frac{4}{1}\))²

\(\frac{Area\; of\; ΔABC}{Area\; of\; ΔPQR}\) = (\(\frac{16}{1}\))

Therefore, the ratio is 16 : 1.